1.Login to blogger dashboard-->Layout > Page Elements
2.Click on 'Add a Gadget'.
3.Select 'HTML/Javascript' and add the code given below and click save.
<script type="text/javascript">
var browser=navigator.appName;
var b_version=navigator.appVersion;
var version=parseFloat(b_version);
document.write("Browser name: "+ browser);
document.write("<br />");
document.write("Browser version: "+ version);
</script>
Now you are done.
File Under : gadget, java script